The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  8  2  8  2  0  2 12  1  1  2  2  8  1  1  0  1  4  1 12  8  1  1
 0  2  0  6  0  6  4  2  4 14  2 12  0 14  4  6 10  0  2 14  2  6  2 14  2 10  8 14  0  2  8  6  2  2  2  4  2  2 14  0
 0  0 12  0  0  0  4  8  0  4  4  8  4  0 12  4  0 12  0  0  8 12  8  8  0 12 12  4  0  8  8  8  4  0  4  0  8  4  4  8
 0  0  0 12  0  0  0  4  8  4  4  8  4  0  4  0 12  8  8  8  4  0  0  4  4  4  8  8 12  8  4 12  4  0  0  4  4  0  0 12
 0  0  0  0 12  0  0  0  4  4 12  8  8  4  4  8  4 12  4 12  8  4  0  0 12  8  0  0 12 12  4  0  8  4  8  0  4  0  8 12
 0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  8  0  0  8  8  0  0  0  8  8  8  8  0  0  0  0  8  8  0  0  0  8  8  8  0
 0  0  0  0  0  0  8  8  8  0  8  8  0  8  8  8  0  8  8  0  0  0  8  0  0  0  8  0  8  8  0  0  0  0  8  8  8  8  0  8

generates a code of length 40 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+179x^32+44x^33+644x^34+504x^35+1400x^36+1748x^37+3879x^38+4880x^39+6238x^40+4820x^41+3983x^42+1848x^43+1317x^44+428x^45+525x^46+64x^47+193x^48+57x^50+15x^52+1x^56

The gray image is a code over GF(2) with n=320, k=15 and d=128.
This code was found by Heurico 1.16 in 11.6 seconds.